A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?

Think about how you find the average of a list of values: You add up the values, and then divide your total by the number of values.

Working backwards, you need to find the overall total, so that you can divide by 50 to find the overall average. To do this, you need to find the two subtotals.

What was the total, before division, for the thirty-five juniors? What was the total, before division, for the fifteen seniors? So what was the overall total?

Now divide to find the overall average!